Krishna S

This paper presents some results on the accuracy of normal form analysis for large deviations from the stable equilibrium point (SEP) in a power system. The results of studies on the region of convergence of Neumann series, which is required for normal form analysis, are presented. A polynomial function approximation is proposed to model the generator exciter limiter. Studies on the accuracy of higher order normal form analysis for large deviations from SEP are presented. Use of Prony analysis in addition to simulation is proposed for the verification of accuracy.

This paper investigates the accuracy of normal form analysis applied to power systems. The steps involved in the method of normal forms are described. The approximations involved in the method of normal forms which can lead to inaccurate results are given. The accuracy of the method is dependent on the convergence of Neumann series used to obtain the inverse of a matrix in one of the steps. Studies on the convergence of Neumann series are conducted on a SMIB system. The region of convergence of Neumann series in the phase plane is determined.

Normal form analysis is used to assess the nonlinear behavior; it can also be used for siting controllers. Normal form analysis is straight-forward for systems governed by explicit ordinary differential equations. However, the analysis becomes complicated if the governing equations are differential–algebraic. The presence of SVC/STATCOM results in the governing equations for which the normal form analysis is not as straight-forward as that for explicit differential equations. In this paper, it is shown how semi-explicit differential–algebraic equations of index 1 are amenable to normal form analysis. In particular, methods are proposed for normal form analysis in the presence of SVC and STATCOM. Normal form analysis can be used to find the location of SVC and STATCOM that results in the best damping of rotor swings; the results are analyzed by case studies and also compared with the performance obtained by locating SVC and STATCOM using linearization methods.